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Local convergence analysis of augmented Lagrangian method for nonlinear semidefinite programming

Author

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  • Shiwei Wang

    (Chinese Academy of Sciences
    University of Chinese Academy of Science)

  • Chao Ding

    (Chinese Academy of Sciences)

Abstract

The augmented Lagrangian method (ALM) has gained tremendous popularity for its elegant theory and impressive numerical performance since it was proposed by Hestenes and Powell in 1969. It has been widely used in numerous efficient solvers to improve numerical performance to solve many problems. In this paper, without requiring the uniqueness of multipliers, the local (asymptotic Q-superlinear) Q-linear convergence rate of the primal-dual sequences generated by ALM for the nonlinear semidefinite programming is established by assuming the second-order sufficient condition and the semi-isolated calmness of the Karush–Kuhn–Tucker solution under some mild conditions.

Suggested Citation

  • Shiwei Wang & Chao Ding, 2024. "Local convergence analysis of augmented Lagrangian method for nonlinear semidefinite programming," Computational Optimization and Applications, Springer, vol. 87(1), pages 39-81, January.
    • Handle: RePEc:spr:coopap:v:87:y:2024:i:1:d:10.1007_s10589-023-00520-0
    DOI: 10.1007/s10589-023-00520-0
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    References listed on IDEAS

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